Related papers: Towards Vorst's conjecture in positive characteris…

D. J. Benson conjectures that the Castelnuovo-Mumford regularity of a group cohomology ring is always zero. More generally he conjectures that the cohomology ring always has a system of parameters satisfying a property he calls very strong…

We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.

In this article we continue the development of a theory of noncommutative motives. We construct categories of A1-homotopy noncommutative motives, described their universal properties, and compute their spectra of morphisms in terms of…

Using a construction closely related to Waldhausen's $S_\bullet$-construction, we produce a spectrum $K(\mathbf{Var}_{/k})$ whose components model the Grothendieck ring of varieties (over a field $k$) $K_0 (\mathbf{Var}_{/k})$. We then…

We introduce an additive basis of the integral cohomology ring of the Peterson variety which reflects the geometry of certain subvarieties of the Peterson variety. We explain the positivity of the structure constants from a geometric…

We study two different flavours of A^1-homotopy theory in the setting of spectral algebraic geometry, and compare them to classical A^1-homotopy theory. As an application we show that the spectral analogue of Weibel's homotopy invariant…

We study the notion of regular ring in the sense of Vogel, which generalizes the classical notion for non-necessarily coherent rings. We build a class of groups "R" containing Waldhausen's class "Cl" in [Wald78] and study its stability…

We deal with the rigidity conjecture of symbolic powers over regular rings. This was asked by Huneke. Along with our investigation, we confirm a conjecture [7, Conjecture 3.8].

A simple, though rarely considered, thought experiment on relativistic rotation is described in which internal inconsistencies in the theory of relativity seem to arise. These apparent inconsistencies are resolved by appropriate insight…

We use the action of the Bockstein homomorphism on the cohomology ring $H^*(X,\mathbb{Z}_2)$ of a finite-type CW-complex $X$ in order to define the resonance varieties of $X$ in characteristic 2. Much of the theory is done in the more…

We study a natural Hodge theoretic generalization of rational (or $\mathbb{Q}$-)homology manifolds through an invariant ${\rm HRH(Z)}$ where $Z$ is a complex algebraic variety. The defining property of this notion encodes the difference…

We prove several conjectures about the cohomology of Deligne-Lusztig varieties: invariance under conjugation in the braid group, behaviour with respect to translation by the full twist, parity vanishing of the cohomology for the variety…

We show that the local and deterministic mode of description is not only in conflict with the quantum theory, but also with relativity. We argue that elementary relativistic properties of spacetime lead to the emergence of a…

We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized characters of the symmetric group. We prove this conjecture for…

Let $n\geq 0$ and $r>0$ be integers. Let $\mathcal{O}_{X, x}^{h}$ be the henselization of the local ring $\mathcal{O}_{X, x}$ of a scheme $X$ at a point $x\in X$. For a normal crossing variety $Y$ over the spectrum of a field $k$ of…

We prove that if $X \to Y$ is a (geometrically) regular morphism of Noetherian schemes, then from a Nisnevich-local perspective, the Gersten complex for Quillen $K$-theory on $X$ becomes acyclic in degrees beyond the Krull dimension of $Y$.…

We associate an $(n_1+\dots+n_t-k(t-1))$-fold Pfister form to any $t$-tuple of $k$-linked Pfister forms of dimensions $2^{n_1},\dots,2^{n_t}$, and prove its invariance under the different symbol presentations of the forms with a common…

We start with a curve over an algebraically closed ground field of positive characteristic $p>0$. By using specialization techniques, under suitable natural coprimality conditions, we prove a cohomological Simpson Correspondence between the…

Let $G$ be a reflection group acting on a vector space $V$ and let $\gamma$ be an automorphism of $V$ normalising $G$. We study how $\gamma$ acts on invariants and covariants (for various representations) of $G$, and properties of its…

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let $Y\ra X$ be a covariant morphism…